Bevel-gearing.



H. D. WILLIAMS.

BBVEL GBARING:

APPLICATION FILED 111111.14, 1913.

1,1 12,509. Patented ont. 6, 1914.

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H. D. WILLIAMS. B'EVBL GBARING. APPLIUATIO FILED APR. 1A, 1913.

l, 1 12,509., Patented Oct. 6, 1914.

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H. D. WILLIAMS.

BEVBL GEARING.

APPLICATION FILED APR. 14. uns.

1,112,509, Patented 00t.6,1914.

7 SHEETS-SHEET 3.

H. D. WILLIAMS.

l BEVEL Guam@ APPLICATION FILED APR. 14, 1913.. 1,1 12,509 Patented Oct. 6, 1914.

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H. D. WILLIAMS.

BEVEL GEARING.

APPLICATION PPLED APR.14, 1913.

LP 19,5599, Patented 001;. 6, 1914.

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. ,Harvey W'llz'ams ,wg/M7 W'l'rz asses.-

H. D. WILLIAMS.

BEVEL GEARING.

APPLICATION FILED APR. 14, 1913.

Patented Oct. 6, 1914.

7 SHEETS-SHEET 6.

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H. D.. WILLIAMS.

BEVBL GEARING.

APPLICATION HLD APB. 14, 1913.

l pl l 2359 0 Eatented 0013.6, 1914.

'I SHEETS-SHEET 7. ggi, @5i/55 'the quality of the surface.

UNITED STATES PATENT OFFICE.

HARVEY n.l WILLIAMS, OE NEW YORK, N. Y., AssIGNoRTo GEAR IMPROVEMENT COMPANY, INC., or NEW YORK, N. Y., A CORPORATION OE NEW YORK.

BEVEL-GEARING.

Specication of Letters Patent Application led April 14, 1913.

Patented Oct. 6, '1914.

Serial No. 760,861.

T0 all whom t may concern:

Be it known that I, HARVEY D. WILLIAMS, a citizen of the United States, residin in New York City, in the county of New I ork and State of New York, have invented certain new and useful Improvements in Bevel- Gearing, of which the following is a speciiication.

The principal object of this invention is to furnish bevel-gearing organized and adapted for being manufactured of a higher quality or standard of uniformity and precision, than heretofore practicable-within the commercial limitations as to cost, `especially when making the gears in large quantities. In view, therefore, of the increasing demand for bevel-gears of a higher precision at a lower cost, and the practical difliculty and relatively greater cost of maintaining a high precision when the tooth-faces have curved surfaces, I have devised a 'system of bevel-gear construction wherein plane-surfaces may be used for the tooth-faces of the wheel, and have also arranged these plane tooth-faces in pairs in which these planeworking surfaces may be located in longitudinal parallelism, so that the wheel-teeth may be made by single-reproduction, and without requiring diflicult or expensive methods or appliances.

In view of the intricate kinematical relations involved in the art of bevel-gearing,

4and to facilitate a clear presentation of the distinguishing features of my present improvements, I have herein employed the term wheel forv designating the bevelgear having the teeth thereof provided with the plane-surface working-faces,.and have designated the mating gear as thefpinion, without regard, however, to their relative actual sizes but having in mind that usually the wheel is larger than the pinion, and that while either one may be used as the driver,

the smaller said., gear will preferably and usually be the pinion and be employed as 'the driving member of the pair of gears.

It is well known that in mechanism generally,"plane-surfaces if not of large size (and with the exception, possibly, of small cylinders), are producible in duplicate in large numbers with the greatest facility and economy and within the minimum practicable limit of variation in precision and in According, in my improved bevel-gearing, I provide the larger member, or Wheel with workingfaces 1n the form of precisionized planes,

and arrange these plane-surfaces in longiwhich are both producible and repairable by the use of simple and ordinary appliances, and Without the use of the complex and expensive generating machinesV for forming or shaping the tooth-faces. Vhile the Well-known epicycloidal and vinvolutesystems of gear-teeth construction,

as applied to the conically modified teeth of bevel-gears, have always been recognized as being radically diii'erent and distant, the one from the other,-and both' different from Willis odontograph nsy ste m,---yet the difference between any two of these kinds of bevel-gears is clearly less, both practically and theoretically, than is the difference between either one of those systems and the system which .I have herein illustrated and explained. For instance, in both the epicycloidal system and the involute system, the cross-sectional profile of the tooth-face is some kind of a rolled-curve, thus making the two systems alike in one oftheir principal features. In my present system, on the contrary, no kind of rolled curvesare used in either wheel or pinion;

curved profile-lines of any kind are not used on one gear of the pair; and, the conicalmodification of the teeth as used in those old systems, is here entirely discarded.

In Order to fully understand the nature and scope ofthe present improvements, it should be remembered that ar very great proportion of all those kinds of bevel-gears which are now duplicated in large numbers, have the pitch-cone ratio of pinion and wheel within the approximate limits of one-to-two and one-to-four, and that this range of proportions applies to such bevel-gearing as employed in many standard 'and special machines, and particularly in automobiles. Also, it will be remembered, that generally the rate of wear of the teeth On the two gears, respectively, is substantially in inverse proportion to the numbers of teeth thereon. Illhus in a pair of bevel-gears having respectively twenty and sixty teeth, the wear' of the teeth on the twenty-tooth pinion evidently would be normally three times as great as on the sixtytooth wheel. rlhus the more rapid wear of the teeth of the smaller wheel, tends to continuously maintain and shape these teethto the proper conjugate form for working correctly with the teeth of the larger wheel. yAssuming that the 'gear and pinion ratios y average one to three, then it is evident that three-fourths of the whole number ofteeth, in this kind of gearing, can now be -made without the use of generating machines, and without employing the evolution method,.and still have the gears operate as truly and accurately as if the teeth of yboth. gears were made by that method'in geartooth generating machines.

Vhile the present improvements are not intended for use in bevel-gears of some proportions and sima-especially as regards the ratio of pitch-circles and the relative numbers and sizes of the teeth,-these restrictions in the range of applicability are Y accompanied by important advantages,-not

otherwise or heretofore practically obtainable,in mode of operation and facility of manufacture in kinds of bevel-gearing which have become of the greatest commercial importance; and thus l utilize to y the advantage of a large class of cases, cerfrom the plane of rotation of' the wheel.'

In this system -of bevel-gearing, therefore, one bevel master-wheel may be practically and successfully employed in mesh with pinions of diderent diameters and conevangles, and with pinions having their coneaxes 1n the `plane of or divergent from the plane of the master-wheel axis.. ln this system, all of the bevel-gear wheels which are of some one given pitch,-especially when the cone-angle of thewheel which is within the range (as hereinafter described) of the .major-cones,`-may have their teeth, or

tooth-spaces, as nthe case may be, all of the same size and shape, all of the mating pinions being, preferably, such as have their cone-angle within the range of the. minorcones of the system, these several terms vand. features. being' hereinafter explained and dened by the description in connection arianne with diagrammatic drawings illustratin the same.

For more readily explaining and distinguishing the nature and scope of my invention, l have in the accompanying drawings forming a part of this specification, illustrated the principles and structural featuresv of the gearing in connection with geometrical representations `of the wheelincluding sphere and certain of its greatcircles, thus following the well-known graphical method usually adopted by. the. leading authorities on kinematics.

ln. the drawings, Figure 1 is a side view of a partially-formed conical bevel-gear wheel, B, with geometrical delineations of the wheel-including sphere, D, and of the circles and lines (including the great-circles 2' and 4), relating to the derivation of the master-form for, and the location of, the

with the skew-angle of the master-form axis reduced substantially to zero. Fig. 2 is-a plane-surface tooth-faces of the wheel, and .y

plan view of the features shown in Fig. 1,

as seen from above in that view, andV further illustrates the feature of parallelism in the tooth-surfaces. Fig. 3 is a side view as seen from the left-hand in Fig. 2. Fig. 4 is an oblique side view of the features illustrated in Figs. 1, 2 and 3, (but with certain additions thereto) as seen fromthe direction of the arrow r1, in Fig. 3. Fig. 4*L isa fragmentary and enlarged view further illustrating` the features shown in the middle part of Fig. 4, particularly as to the location on the sphere D of the profiles of the wheel and pinion teeth; this view is drawn with the master form axis in alinement with the same axis in Fig. 4,' to facilitate comparison. Fig. 4b is a view similar to, and is drawn in alinement above, Fig. 4, for showing how the odset-circles, as 3", 5b, may be odset from the intersecting great-circles 2 and 4, respectively, in reversed directions from this arrangement in Figs. 1, 4 and 4a, for bringing -the planes of the tooth faces into the outwardly-converging construction. Fig. 5 is a side view ,similar to Fig. 1, but showing the o'set planes (as 3 and 5, Figs. l, 2, 3 and 4) of the tooth faces, as being odset or swung into an angular or skew position,`-fo'r thereby giving a substantial skew-angleto the axis, m4, without any Substantial change in the tooth prole. Fig. 6 is an oblique side view, analogous to Fig. l, but asseen from the direction and at the angle ofthe arrow 13, Figs. 3 and 5, skew-angle of the masterform-axis is not reduced to zero; in thisA View the master-form F* is shown skew-1ocated and as having the same skew-angle as shown in Fig. 5. Fig. 7 is a fragmentary plain view of the middle portion of Figs. 5

and 6, as seenin the direction of thearrow w8, Figs. 3 and 5, for more clearly showing the skew-angle, e, corresponding with the tangency or skew-circle t, in said Figs. 5 and 6,also in Fig. 9. Fig. 8 is a diagrammatic view similar to the right-hand portion of Fig. 3, for showing certain relations between the wheel, (here designated as B2) and a co-meshing pinion of non-normal proportions. Fig. 9 is a diagrammatic perspective view similar to Fig. 6,-and as seen in the direction of the arrow ri in Fig. 8,-for further illustrating the skew location of the wheel teeth, and how this form of wheel, as B2, may be operated- .with a, skew-located pinion'of non-normal proportions, particularly when the skew-angles of master-form axis and pinion axis, respectively, are oppositely located relatively to the wheel axis. Fig. 10 is a view of a portion of Fig. 9, but shows the parts as seen in the direction of the arrow r6 in Fig. 8. Fig. 10a is a fragmentary plan view (comparable with Fig. 7) of a portion of Fig. 10,

but is drawn in projection with and below Fig. 8, for more clearly indicating certain features shown in the companion views, Figs. 8, 9 and 10, of this group of the drawa ings. Fig. 11 is a sectionalview showing the wheel B, (which may also correspondy with the forms B* or B2 thereof) and a plurality of pinions operable` therewith and Vincluding pinions of normal and non-normal proportions. Fig. 12 is a diagram corresponding to Fig. 3 and to Fig. 3b, for illustrating the making of any plurality of bevelwheels all having the same pitch and one size and form of tooth, whatever may be the diameter of the tooth-circles of the several wheels, of which five different-specific cases are shown, all Adesignated as the wheel B,

and individually distinguished by the reference characters Ba, Bb', Bc, Bd and Ba. This range of wheel-cones, as' here illustrated, extends from the cone-angle of 45 degrees, (equal to an inclusive angle of 90 degrees),\from the line in wheel BJ, and .upwardly therefrom to any cone-angle below the line 13, (which indicates a plane of revolution), and this range of the larger cone-angles is herein, for convenience, designated as the range ofthe major-cones. These several proportional variations inthe wheel B are further illustrated in Figs. 12a to-12e inclusive, each showing a short portion of the tooth zone N as seen in a direction vertically thereto. Fig. 121,- for instance, shows part ofthe wheel B as seen in the direction of arrow 12", Fig. 12, and with the cone-face length, from e to 8, laid off from the axial line w3 4as a meridian for these views. Fig. 12b-similarly shows the cone-length and the pitch ,angles of ywheel Bl. The same features of wheel Bc are shown in Fig. 12"; of wheel Bd, in Fig. 12d;

-ofwheel Be, in Fig. 12e. In these views the smaller wheelsB, B", Bv?, are of-fthe same diameter; wheels Bb and Ba are of the same have their pitch circles located the same distance, 12f, from the equatorial plane 13, through the apex c, which is common to the normal pitch-cones of all the wheels. The term cone-angle, as here employed usually refersto the inclusive angle, as, for instance, in Fig. 12, where the wheel Bc is indicated as having an inclusive angle of ninety degrees, while the cone-angles of the other wheels as Ba, Be, are all much larger. Figs. 13 and 13@L are views similar to Figs. 4a and 4b, respectively,l for illustrating the two arrangements of the tooth-planes convergence, and for explaining certain operational features thereof, in connection with Figs. 12 to 12?, and other preceding views. p Figs. 14

and 14a are two connected views together Y and drawn in projection with Fig. 15 fory more clearly showing the skew-location and the circumferential advance of the toothsurfaces. Fig. 16 is plan-view diagram corresponding with Fi 2 for illustrating the progressive meshing of the pinion teeth with the tooth-faces of the wheel, and Figs.

16a and 16b are connected diagrams supplemental to F ig. 16 for furth r illustrating the same features as taking pliice during the passage of a wheel-tooth through the usual arcof-'approach; in Figs. 15 and 16,- the views are taken in the direction of the arrow 1', Fig. 3.. Fig. 17 is a view similar to a portion'of Fig. 3, for indicating the initial stage of the progressive meshing as occuring 0n the inner circle ofthe tooth-zone, as hereinafter explained in connection with Figs.`

16, 16a and 16h; and Fig.,18 is a similar view showing the same stage, as occurring on the outer circle of the tooth-zone of the wheel, when this has the improved master-form F in which the planes of the tooth faces are arranged with the inward convergence, as shown,-for, comparisomin Figs. 15 and 15a. Figs. 19 and 2O are diagrams further illustrating certain features of the meshing gears, especially the line-bearing engagement of the pinionv tooth-faces with the wardly-converging, as in sive, and in Figs.- 5, 6, 7,

4bevel-gears will usually great-circles,

plane-surface faces of the wheel teeth. Figs. 21, 22 and 23 are diagrammatic views illustrative of the preferred method of making the gears when the wheel B (or any form thereof) has the tooth-face planes in- Figs. 1 to 4B, inclus,9,10,10,1s and 14. Figs. 24 and 25 are views similar to Figs. 21 and 23, respectively, for .Similarly illustrating the method when applied to the making of gears in which the said toothface planes are outwardly-converging, as in v Figs. 4", 13a and 14a. Fig. 26 isa side view, chiefiy diagrammatic, of the pinion, F, as seen from the left-hand in Fig.- 25; these two views are drawn in alinement to facilitate the comparison thereof. Fig. 27, is a face view of a portion of the pinion as seen from above in Fig. 26, with this difference however, that the tooth-zone is here shown as if the pitch-surface, (the geometric cone of revolution formed by the tooth-form axis, as Figs. 3, 19 and 22, when revolved about thepinion-axis m, Figs. 3 and 23), were enrolled into a plane, for thereby bringing all the pinion-teeth to stand as if vertically disposed in ,a plan view, to facilitate description and comparison. Fig. 28, is a view in all respects similar to Fig` 27, with the exception, that whereas in'Fig; 27 the geometric master-form is applied to the toothspaces, (in correspondence with Figs. 24, 25, and with Figs. 4", 13 and 14), this masterform is here shown applied in Fig. 28, to the pinion-teeth, thus producing the form of .pinion-tooth having the longitudinally-parallel construction or conguration and vwith I the intervening -tooth-spaces of the longitudinally-tapering formation. Fig. 27 is an enlarged fragmentary view showing a pair of pinion teeth corresponding to those indicated in Fig. 27, as seen inthe direction of the arrow in Fig. 26. Fig. 28a is `a view similar to Fig. 27, but showing pinion teeth' and spaces arranged as in Fig. 28,\and with these teethhaving their wheel-engaging surfaces conforming Ato the compound-reproduction configuration, which is hereinafter more fully explained.

Similar characters all the views. e

ln this improved bevel-gearing, a pair of comprise a conical wheel having plane-surface tooth-faces ardesignate like parts in Aranged in parallel with an axis which at its outer end colncides with the intersection of two great-circles of a wheel-including sphereto the center of which said axis may have, relatively, a skew-location.l The said toothface planes lie in the planes of two circles which are, respectively, parallel to said and may be offset by equal outwardly therefrom, thereby distances thwlse armaking the longitudinal, or len allelism to the tooth-spaces oft ly-converging e whee Maratea Before proceeding detailed description, that of the two arrangements of the system herein illustrated, the transverse convergence of the longitudinally-parallel planes which is shown in Figs. 4h and 13a (also indicated in Figs. 14a, 24, and m25 to 278,), is regarded as the primary arrangement, since the figure or master-form, as F1, is here apnplied to the-two plane-surfaces of one toot or tooth-body, which therefore has acrosssectional shape and size, and a coniiguration,

to more complete and it should be understood coinciding with said master-form. Thus in the primary arrangement or organization, the said master-form may be said to be the tooth-form, or to coincide therewith, and vice-versa. In the secondary and improved arrangement, as shown for instance in- Figs. 1 to 4, (and in other gures elsewhere herein more fullycxplained), the same tooth-.form ligure or 1naster-form, as F, Figs. 4a and 13,-d (which may also be defined as a systemform, and tooth-surface generant), is shown applied in a reversed manner to the inwardand adjacent plane-surfaces, as f3 and f5 (Figs. 4, 4a), which are the two bounding planes of a tooth-space having the longitudinalparallelism; and-each of these two space-bounding planes isfalso a bounding plane of a tooth having a longitudinalangle greater than the angle subtended by the pitch-arc, (see diagrams Figs. 15 and 16 and the description therof). in the said primary organization, therefore, the master- -fo-rm, (see Fig. 4b), directly coincides with the pair of geometric plane-surfacesl-these being in the longitudinal-parallelism,-in which lie the pinion-engaging tooth-surfaces, as f3 and f5", (Fig. 4"), of the wheelteeth. But in said secondary arrangement, the same master-form, Fig. 4a, is shown applied in a reverse manner to a different pair of the geometric plane-(surfacesf-these also being in longitudinal-parallelism,--in which lie the inwardly-converging and 'adjacent pinion-engaging tooth-surfaces, as f3 and f5, respectively, of two adjacent wheel-teeth, each 'of' which has a.y longitudinal-angle greater than the angle subtended by the pitch-arc, (see Figs. 1 2, 15 and 16 and the description thereof). Thus in both the primaryv and secondary organizations the series o-ftooth-'surface planes are arranged in two series of pairs, and in each said organization' the pairsl of one series have their planes vin longitudinal-parallelism, while the. planes'of the other series have a longitudinal-angle greater than the angle subtended by the pitch-arc.

A' master-wheel made according to either said organizatiomthe primaryor the secondary,-has the pinion-engaging tooth-surfaces -thereof consisting of plane-surfaces arranged in successive pairs 1n which each pair has the planes thereof transversely converging, and also in longitudinal-parallelism and conforming to the' single-reproduction configuration; and a co-meshing conical pinion for operating in combination with either form of su`ch master-wheel, will, conversely, have the wheel-engaging tooth-surfaces thereof curved to conform to a corresponding compound-reproduction configuration, (see especially Figs. 21 and 28a, inclusive, and the description thereof.)

The form or configuration of a toothsurface maybe said to include the features of outline, or profile, and the relative position thereof. The character of the prole depends, of course, on the kind of reproduction, whether single, (as in the case of the \vl1eel),-or compound,' as in the case of the pinion; the position depending on the direction of the transverse convergence, whether inwardly or outwardly,-in one manner in the case of the primary arrangement, and in the reverse manner in the case of the reversed and secondary or improved arrangement. As thus applied to the wheel, each profile or side-line, (as f3 or f5, Fig. 4a, of the form F), gives,-always by the same direct rep1oduction,the shape or profile, and also the position or angular relation, to one tooth-surface in each said arrangement of the wheel construction. In the primary arrangement, the said master-form,-as represented in a tool (as T, Fig. 24:), that is coincident therewith-and by the use of the single-reproduction method, produces a pair -of tooth-surfaces bounding the body of one and the same tooth, (Fig. 4b), and therefore gives to this tooth an actual sectional shape and size which is the exact counterpart of said master-forni. In the secondary arrangement, the same results as to outline and relative position (Fig. 4a) are produced (as by the tooth J, Figs. 21, 22), on the two adjacent tooth-surfaces ofA two adjacent tooth bodies, respectively, but with the sectional shape and size applied to the toothspaces. I

It will be remembered that the custom of making a tooth section symmetrical with a central line, as Z, Figs. 13 and 13, vertical to the plane of rotation, is for the purpose of enabling the gear wheels to be operated equally well ineither direction. But when the wheels are running in some one direction (as, for instance, in the direction of the arrow 717 ,'Fig. 16), only the rearward faces, as )caf-see Figs. 13, 14, 15,-(or when the tooth-form is 'reversed,the faces f3", Figs. 13a, 1-15) are the driving-faces of the wheel-teeth, in cases where this wheel, as B, is the driven member of the pain-while the opposite faces, as f5 (or, 7651 in the said Figs. 13, 14a), operate for preventing an irregularity of movement because of any tendency to throw the`.wheels forwardly too rapidly, thereby regulating the rotary move-'- ments of the wheel and pinion with precision. Thus the actual driving of the wheel B by the pinion P only involves the said rearwardly-acting driving-faces of the wheel B (which I designate as actionfaces and the forwardly-acting or driving-pressure faces of the pinion P.

To simplify the description and, also the statement of the combination claimed, the wheel-tooth working-surfaces are herein usually referred to without particular mention of or reference to the areas,-respec tively above and below the pitch-line 7 which constitute the face proper, and the Hank of the working-surface, as illus-l trated in many of the figures of the drawings. For instance, as shown in Fig. 4a each tooth-face, as f3, is shown extending on the' line 3 above and also below the pitch-line 7, which thus divides that working-surface into the face ortion, or zone,'lying between the lines )if and 8, and the flank portion or zone lying below said pitch-line 7. Since these two Zones,the face and the flank ,-are herein shown and described as located,-in any one tooth-surface,-in one continuing plane, they may as regards some features be considered as a single mechanical element or component of the wheel, but as regards other features, they are separate tooth-face components, especially as related to the path-of-action, since the face one is only effective within the arc-of-approach (before reaching the instamt-axis) while the flank is effective during the passage thereof through the arcof-recess, after passing the instant axis.

Since the lower pa'rt of the tooth-space is needed for clearance to allow the passage of the point of the pinion-tooth,as customary in the ordinary kinds of faceand-ank toothed-gearingtherefore only a part of the width of the flank-Zone, (when made as shown in Figs. 4, 4a and 19, for in stance) will be actually used as a workingsurface, so that, in practice, the width of the face-Zone relatively to the width of such working-portion of the Hank-zone, may ordinarily be fixed at a ratio of about one to two,-this being about the ratio herein illustrated. 'This construction has the advantage of providing a relatively long arcof-approach during which to first accomplish the progressive meshing t (hereinafter more fully defined and described) and then secure in each pair of the contacting driving faces, an effective kind and large measure of driving action while the line-ofcontact is still outsideof the geometric pitch-surface and before it reaches the instant axis. This construction, by reason of the special operational features here referred to, also provides for such ailextended path-of-action as to securethe proper co-action with ythe driving tooth-surfaces of a plurality ofI the opposing, or re-action, tooth-surfaces, as hereinafter more fully explained.

My present invention contemplates a system of bevel-gear construction in which all the wheels of a given pitch, and of whatever size of pitch-circle, may have acted-on or driving-faces located on any' given skewcircle relatively `to the wheel axis, and' located all in `one angular or skew-relation to the cone-angle of the wheel, whatever may be' the size or cone-angle of the wheel in any given instance, (within the described range of wheel proportions.) And, similarly in any such wheel, the reaction faces, as f5 (or f5, Fig. 13) of the teeth may all have the same skew-angle, which may be equal to the action-face skew-circle and skew-angle. The aforesaid directly-coacting facesbeing arranged in converging pairs, and these pairs, as f3, f5, Figs. 13, 111, and fsb, fm, Figs. 13a,

14a, being alike except as to the direction of the convergence, each such pair of the converging faces are located or produced lin accordance with a eometric feature which l designate as the master form. As shown in Figs. 13a, 14a, said master-form planes as reproduced in the faces, f3?, f5, are outwardlyconverging, whereas in Figs. 13 and 14 (as in Figs. 1 to 4), similar faces f3, f5, have an inward convergence. For convenience, the said pairs of wheel tooth-faces-as f3 and f5,are herein considered, in a mechanical sense, as being tooth-form faces, since they coincide with the geometric tooth-form as reproduced by a single movement (and without rotation) along and parallel to a straight line path, as for instance, parallel to the axial line ai-see Figs'.v 1, 2, 3, 22. This mode of reproducing thev geometric tooth-form in the plane-surface wheel-tooth faces, lf designate as single-reproduction and these faces when so produced l designate, in and for the purposes of this application, as parallel in parallelism or longitudinally-parallel, or as having longitudinal parallelism, since these said faces when so reproduced have surface-element lines parallel to the said Straight-line path of movement, and also have these lines in a geometric plane.

In Figs. 13a, 14, (also see Figs. 24, 25), the master-form is shown applied to the wheel-tooth, which thus has the longitudinally parallel faces. In the other said figures the master-form is shown applied -to the tooth-spaces, as F, while the master-face planes,as f3, 72,-- are shown odset in parallel from the tooth-form axis,

In each of the described arrangements of the convergence of the wheel tooth-surfacev planes,-as indicated for instance in Figs.

' 14 and 14",' respectively,these Wheel-tooth faces, (in any series of the tooth-faces hav- 'ing the longitudinally parallel construction) iniaaoa are so arranged and related that,-as shown in Fig. 12"-,-.in any group of three successivetooth-faces, two of these are arranged in longitudinal parallelism with each other, and since in practice at least three successive wheel-tooth faces will be in mesh to the extent of having a working engagement, therefore at all times in such a set of three suc'- cessive faces there is a direct parallel (di-y rectly opposite) action and re-action, respectively, upon a pair of longitudinally-parallel faces which are one of them next succeeding to the other of them in the circumferential tooth-Zone N of the Wheel. This peculiar relationship and mode of coaction, is indicated in Figs. 15, 16, and other views, and particularly in said Fig. 1.2, where the two inwardly-converging successive faces 21 and 22 are in parallel, while the next successive face, 23, is at an angle, as Z2, thereto. Also in said Fig. 12, another set of three successive faces comprises the two outwardly-converging longitudinal nonparallel faces 23, 23, and the next succeeding parallelly-disposed face 24. In each of these two, the directly opposite action and co action is indicated by the'longitudinal parallelism of the two oppositely-acting faces, as 2l, 22, in the one set, and 23, 24 in the other set. ln this form of the wheel, (as B, Figs. 1 and 2) the action-face (as f3, Fig.

' 13; and 22, Fig. 12a) is located between and oppositely inclined to, a pair of re-action faces, as 21 and 23, Fig. 12, of which one, as 2l, is longitudinally parallel to that action-face, while the other said re-action face, as 23, is inclined to said action-face 22 and also to said reaction-face 21. Thus the one action-face, as 22, coacts with two re-action faces,of which one is longitudinally-parallel and the other longitudinally non-parallel therewith, so arranged that the progressive-meshing of the two reaction faces is different in the one than in the other (see Figs. 15 to 18) While at anyone moment the direction of the one reaction is oblique to the direction of the other reaction; and relatively to the 'action-force itself, the one reaction is parallel to the actionforce while the other said yreaction is oblique or inclined to such actionforce,- so that at all times during any considerable meshing arc, the action-force on each action-face is accomplished by a plurality of reaction forces of which one is divergent from another, and of which one is parallel to the said action-force.

When the master-form, as F, is located (see Figs. 1, 2, 15) with its central line or axis w, in a plane radial tothe wheel-axis ai, and when. at the same time the pair of tooth-faces, as f3, f5, outwardly from the inner-circle 6 are longitudinally-converging relatively to the radii Z3 and Z4, respectively,

as shown in Fig. 15, then the action face f3' has a rearward deflection or skew-angle Z5, and the re-action face f5 has a forward deflection or skew-angle Z5. In practice (and except in skew-gearing) these forward and rearward tooth-face skew-angles are preferably equal and of such amplitude 'as to bring the tooth-face surface-elements into parallelism, since this construction and arrangement greatly facilitates the economical manufacture and also the'maintenance of the wheel teeth, in the manner and for the reasons elsewhere herein more fully set forth.

In the class of bevel-gearing, and within the relative ranges, to which my present improveniente are more especially applicable, the pinion is almost universally employed as the driving member of the pair, while the larger gear, or wheel proper, is the driven member of the pair, and accordingly it is an especial object of my invention to furnish such bevel-gearing in which,-contrary to the practice heretofore,-the pressure-angle of the driving pinion teeth against the teeth of the driven wheel, may be a constant angle regardless of the cone-angle of the wheel and also regardless of the particular kind of pinion, within the ran-ge developable from such wheel teeth. This feature is illustrated by Figs. 13 and 13a, in which the arrow r2, showingthe direction of th at constant angle of the driving pressure against the fiat tooth-face f3, is located normal (vertically) to said face, thus giving a maximum steadiness'of rotation to the driven wheel and to any mechanism operatively connected therewith.

In the usual forms of bevel-gear teeth, as shaped by the well known evolution method,-and generally accepted as the standard type for use in gears having the teeth thereof formed by a metal-working `OperatiOm-there is, some proportionate dimension or ratio which applies asbetween the transverse tooth-section at the oute` and larger end of the tooth and the outer pitchcircle; and which also applies .as between the tooth-section at the inner end of the tooth and the inner pitch circle, since in such gearing all the tooth-face surface-element lines extend to one point of origin, which in general practice (except in skewbevels) is the point of axes-intersection. That uniformity of ratio as between the transverse tooth-section at any point in the length of the tapering tooth, and the corresponding pitch-cone circle, is radiically departed from in the pair of bevel-gears herein illustrated.- In these gears, one of the wheels has a tooth-section of uniform character and of a variable section-andcircle ratio, while in the mating wheel the teeth have both a variable tooth-section and a variable said ratio as between such teethsections at successive points along the length of the teeth, and the corresponding pitchcone circles. Furthermore, these ratios are variable in opposite directions, respectively,

'in the wheel and in the pinion. When the wheel in Fig.l 14a) has the uniform-section teeth, the said section-and-circle ratio is such that the tooth-section is relatively smallestv at their outer ends at the. outer circle, and is relatively largest at their inner ends, at the inner circle; but, contrary to those relative ratios, the teeth of the mating pinion P will then have their tooth-section relatively largest at their outer ends, and relatively smallest at their inner ends, at the inner and smaller circle. Thus the said scction-and-circle ratios in the wheel and pinion, respectively; are variable in opposite directions along vthe length of the teeth.

By the term transverse as herein used for designating the convergence of the two faces comprised in a pair of longitudinally parallel tooth-faces I refer to that direction which is transverse to the lengthwisedimension of the tooth.l For instance, in Figs. 1, 2 and 14, the lines v3 are located transverse of the tooth-faces, f3, the length of which extends from the inner tooth-circle 6 to the outer circle 8. Also in these figures, the convergence of the two4 tooth-faces f3 and f5 is shown of the inwardly converging arrangement, since those surfaces if continued below the base of the teeth will meet, as at 155, below -the space F, or within the space inclosed 4by conical pitch-surface of the wheel. In Fig. 14a, the tooth-face transverse convergence is outwardly, Since the faces feb and fb, when continued upwardly, will meet at the line Z5, this line being now located 'externally of the conical pitch surface of the wheel. V

In establishing the proportions and l0- cation of the master-form for any given master-wheel, we may'proceed as follows: Vith any sphere-axis, as m3, Figs. 1 and 2, tix the sphere-center at c, and lay olf the required sphere-radius, as at the angle required for the normal instant-axis, and develop the geometric wheel-inclosing sphere, D, concentric to said center c, and with the said aXis w, as the radius. Through the axis-point m, on the surface of the geometric sphere, lay off the two"greatcircles 2 and 4, intersecting at said axis-point and making the angle, (as Z7, Fig. 14) required for the selectedor proposed master-form. From the axis-point now layoff the normals ZS, Z", Fig. 19, of the length required for the normals from the tooth-faces to the said instant-axis and 'next draw the small-circles 3 and 5 parallel to said greatcircles 2 and 4, respectively, and at the distancefrom these great-circles indicated by said normals Z8, Z9. Then will the vplanesurfaces of the required tooth-faces lie in` lll 3 and 5; and also all the arallel surfaceelements of said tooth sur aces will be arranged in parallel with the said instantaxis .r, of the geometric /wheel structure. llhe foregoing geometrical construction being developed, the wheel structure itself may then be readily drawn, the tooth-profile outlines, as F, being repeated around the sphere, asmany times as the pitch may require.

In the said offset planes, the areas of the wheel-tooth-faces,-as to the lines (surface elements) thereof in parallel with the axis fbg-are, when taken together, non-radial relatively to the wheel axis, even when said axis is locatedl in a plane which is radial to the Wheel axis. This feature will be evident from a comparison of Figs. l to 4, in which -the axis ai is located in a plane radial to the wheel-axis :113. And owing to the convergent positions, as already explained, of the toothface planes, it will also now be evident that in any case, and whatever may be the skew-v angle of the form-axis a', only one such surface-element of any one air of such faceplanes can be radial to t e wheel-axis ma; and, hence, as already indicated, all of lthose convergent plane-surface tooth-faces always have a skew-relation to each other and to any plane of the wheelaxis, and also have a corresponding skew-action or operational relation to the instant-axis of each of the geometric pitch-surfaces of the pair of gears.

A For more clearly illustrating the' feature of the master form as herein employed, andespecially in connection with the feature of skew relations, 'a master form cone is indicated at t in Figs. 7, 9, 10, 10a-and 121. The direction of this cone corresponds with the convergence of the two faces. (as f3 and f5) of each duplicate outline-form, whether these faces converge outwardly, -as in the case of longitudinally parallel teeth, (Figs. 13, 141), or converge inwardly, as 1n the case of the further improved and preferred lconstructionr having longitudinally parallel spaces. ln Figs. 9, 10 and 1011, the toothform cone t is shown with its axis located to one side of the wheel-center 'cl by the distance Z10 which may be varied to give'the desired amount of skew in any given case.

In Figs. 9 and 10 the skew-angle Z1? is shown at 'the right-hand of the line QR, representing an axial-plane of the wheel axis, while the pinion-axis skew-angle e8 is on the left-hand of said plane, this being a preferred organization for the reason among Y others that (when .the pinion is the driver) .the pressure against the wheel-teeth Ifaces tends to counteract the usual tendency of a bevel pinion to crowd outwardly from the wheel axis. p

When the axis of the form cone t, as in Fig. 12, coincides with the wheel ax'is at c, thecircle t1 of [said forni-cone is the skewiuiaaoe circle to which are tangentially directed the upper lines, as Z1* and Z15, of the respective tooth faces, f3, f5, and, similarly, thesmaller circle'zf3 of said cone t is then the skew-circle to which are directed the lower lines, Z1, Z1?, of said tooth-form faces. 'llhus the faces of the wheel teeth (as also illust-rated in Fig. l5) are skew-located even when the master form-axis has its own skew-angle reduced substantially to Zero.

"When the pinion-axis skew-angle, as e8, Fig. 10, is greater than the pitch-angle e of the wheel,-especially when the pinion, as P4, is of plus-normal. size, and has its coneface longer than the wheel-cone face,and when the skew advance of the wheel-teeth outwardly is toward the approaching teeth of the wheel, (as indicated in Fig. 10) the angular width of the zone of progressivemeshing as regards any single tooth is lnormally 4largely increased, (see Figs. 15 and 16) with the result of bringing the initial tooth-mesh earlier, and reducing the rate of outward movement of the path of the contacting point of the engaging surfaces, this lpath being normally a nearly straight line.

Thus by means of the present improvements, l furnish a pair of gears in which both the wheel and pinion are conical, and which are skew-bevels in arrangement and mode of action, and in which, nevertheless, the wheel," as to thecenter lines of its teeth,-may be of non-skew and conical construction, thereby securing a superior mode and quality of action combined with the simplest and most eoy advantageous forms and characteristics as to the practical use and manufacture thereof; and with the additional feature thatr such wheel of the skew-bevel pair is also ra master-wheel which is eqiially operable with non-skew pinions, and with these of the vavious kinds and arrangements as elsewhere herein more fully explained.

ln 'ordinary-practica nearly all pairs of bevel gears may be properlyl regarded as skew-bevels, since the wheel-axis and pinion-y axis seldom meet exactly, and in nearly all instances there is also, geometrically, an actual skew-circle, having a small but material diameter. -ln View of these circumstances, l use theV term radial as applied to the relation of pinion-axis to the wheelaxis, for indicating a case in which the axial skew is reduced, not necessarily nearly to any absolute zero, but merelyto some compara-v tively small proportion of the pitch-arc, as for instance from one to ten per cent. thereof. The skewarrangement of bevel-gears may therefore be regarded as the usual one, and also as the general arrangement or class within which the said radial arrangement of pinion axis is only a particular case. And this ,view applies also, andv for similar reasons, to the location of the master-form axes on or relatively to the wheel and pinion cones as regards the size and location of such a geometric skew-circle.

In a pair of bevel-gears the pinion axis, as Figs. 9 to 10a, may be considered as being always located tangential to a circle, c7, concentric with the wheel axis-m3. When said tangential or skew-circle, 0", has a substantial diameter, the gears are then skew-bevels, the extent of the skew, or axial divergence being the skew-angle e8, Fig. 10; andwhen said skew-circle 07 is reduced to zero, the bevel-wheels become non-skew, (seeFigs. 8 and 4) since the axis of the wheel and the axis of the pinion will then lie both in one and the same plane. In this system of bevelgearing, however, in a pair of skew-bevels, in some cases only the pinion may have the skewed construction, while the master-wheel remains ofthe same conical form as provided for use with the non-skew pinions, thus securing an important advantage not heretofore, so far as Ifam aware, obtainable in skew-bevel gearing. Thus, in this system, all of the pinions may be considered as belonging to one class, the skewbevel kind, the extent of the skew-angle or axial divergence being reducible to any required amount, with zero as the limit of such reduction.

In the arrangement or relativelocations, of wheel-axis and pinion-axis in Figs. 3 and 4, in which these axes are not shown with any substantial amount of axial skew, and also in the arrangement shown in Figs. 8 to 10a, 'in which said axes have a relatively large amount of axial skew, there is one feature or relation which is the same in both cases, viz the direction of the wheel-axis, as located in a plane which is parallel to the pinion-axis, is transverse to the direction of the pinion-axis as located in a plane which is parallel to the wheel-axis, and this constancy of directional relation obtains when the two axes are in one plane, and alsowhen each is in a different plane of a pair of parallel planes. In the figures here mentioned the said transverse ydirections (see Figs. 3 and 8) are indicated as being substantially at right-angles, the one relatively to the other. And, as will now be evident, the said transverse relation of the two axial directions will be unchangedby a variation of the amount of the axial skew. In, and for the purposes of, this description and claims in this application, when an axis is located in a given plane, such axis and plane are regarded as being parallel, thel one to the other.

It is generally well'known to practical mechanics that the usual hyperboloidal forms of 'skew-bevel gears, while theoretically suiiciently correct, cannot in practice be successfully produced within a cost limit faces and the faces of a co-meshing t bringing the pinion-axis,

which does not make their use, to any considerable extent, commercially impossible.

their working-faces in the form of the transversely-c'onverging planes, Yand these are arranged in parallel,.so that in any such pair of toothfaces their normal operation involves a skewactionvasbetween these plane-surface toothp1n1on, even when the skew-angle of the masterform (or of its axis Figs. 1 and 2), and also the skew-angle of the pinion-axis are each reduced substantially to zero, thereby as x6, to intersect the wheel-axis, as w3, Fig. 3, and bringing the location of the center lines of the teeth and tooth-spaces of both the wheel and the pinion into substantial coincidence with axial planes that are radial to *the wheelaxis, and pinion-axis, respectively. In this gearing, therefore, there is a certain skewaction of the tooth-faces which is normal to the operatiom-together with a relatively progressive meshing (see Figs.' 15418), longitudinally of the teeth during the approach into full-mesh,.-so that the increasin of the said skew angles or either of them rom zero to within any practicable limits, does not, in eilect, create al diierent kind of coaction, but merely varies in a quantative manner the same kind of co-action which occurs when the gears have the actual skewangles reduced substantially to zero. Thus a skew-action involving a longitudinally-progressive meshing, as between the plane-surface wheel-teeth and the coacting curvedsurface pinion teeth is obtained even when the master-forms. are located radially-to the wheel axis, and with pinions of different sizes and having respectively, ditferentskew locations of the pinion-axis relatively to the Wheel-axis. During this progressive meshing of the coacting teeth, which proceeds after the manner comparatively illustrated in Figs. 17 and 18, in connection with Figs. 1 6l1 and 16, the initial meshing or toothengagement will usually begin at the inner tooth-circle 6 Where the tooth has the lowest velocity and thence proceed outwardly along the tooth to the outer circle 8, where the teeth have .the greatest velocity; and during this period the tooth, :as h, of the wheel B advances circumferentially through some- What less than one-half ofthe arc k, Fig. 16.

A. further feature of practical importance results from the lesser angle subtended by the outer end of the master-form as compared with the angle subtended by the inner end thereof, in that the period is increased within which the best character of direct coaction, within the arc of approach of the tooth-faces is maintained at the outer end of the tooth-faces, as compared with the period and duration of the progressive meshing at theinner end-of *he next following pinion tooth. This advantage will now be evident from a comparison of Figs.

13, 13a, where the driving action, at r2, on

the faces at f3' is kept from reaction by the nearby reaction-faces at f5., this control being prolonged until the inner ends of the next following pairs of faces arewell advanced toward their full mesh position. These advantages are thus related to the circumstance that in this gearing the tooth-faces have a height, and the longitudinally-parallel pairs thereof have a width, which subtends' decreasing angles from the inner tooth-zone circle, 6, (Fig. 15) outwardly to the outer circle 8 of this zone. By reason of the said skew-location or circumferential advance of one end of each tooth-face relatively to the other end thereof, the boundary line, as 30, of the meshing zone ,7c (at the left hand cfsaid zone in Fig. 16) is varied in. location either to4 reduce or increase this zone to some extent from what said zonewidth c would otherwise be; but as the said driving or pressure-face, as f3, approaches the location usually designated as the instant-axis, the` skewdocatio-n of said pressure-face causes the two wheels to operate somewhat after the manner of gears having spiral teeth, and this result is accomplished even while the location of the body of the tooth, as to its center or axial line, as Z, Fig. 13, is ina plane radial to the axis of the wheel. vOn the forward side of the tooth h1, Fig. l15, the reaction face f operates, of course, in a reversed order or direction re1atively to said action face f3, not only as to the approach of the coaching-face of a pinion tooth as at c1, Fig. 16, but also as to the recession or drawing apart of said con acting faces, as at e2, Fig. 16. When the tooth-face-'planes are outwardly-converging, as in Fig. 4", the rearward face, f3", of the pair of tooth-faces is, of course, the driving or pressure-face, while the forward face fm acts as a direct reaction face therefor; but when the tooth-face-planes are inwardlyconverging, as in Figs. 49, 15 and 15,

the forward face f3 is the driving face whilethe rearward face y is the direct reaction face therefor. Thus, circumferentially of ,the wheel, the order of succession of these directly coactin driving and reaction faces is re lersed .in t e vtwo arrangements, respectively, o'f the transverse convergence also,

yplane-surface f5 the skew-angles of the saidl two faces will be similarly reversed, as will be evident from Fig. 15.

One feature of the skew-action of the plane-surface tooth-faces, relates to the increased duration of the meshing period or zone which is obtained 'by arranging the tooth-surface skew reversely to the axial skew of the p-inion and relatively to the direction of rotation. For instance, as shown in Fig. 10, if the axial-skew of pinion-axis a'is assumed to be forwardly (that is swung in the direction of whl rotation as there shown (then the skew ofthe form axis, m2, is rearwardly. And this saine relation l regard as still subsisting when the skewangle of the form-axis (as shown by the angle e7, Fig. 10) is a substantial amount, even when the said pinion-axis skew is reduced nearly or quite to zero, (as in Fig. 3) since in all such non-similar relations of the two skew-angles one result is to modify the meshing-zone arc, as lc, Fig. 16, relatively to what this zone and arc would be in arrangements where the said skew angles are not so reversely located, as shown for instance by Ft in Figs. 5, 6 and 7. By thus varying the skew-arrangement of -pinion axis and master-form axes.l the duration of the progressive meshing period or zone, can be regulated to suit a wide range of requirements, while retaining the planesurface character `and the longitudinally parallel location of the tooth faces of the wheel. With these skew-located or nonradial tooth-faces as arranged in pairs and in parallel with the master-form axis, another peculiar feature of the described progressive-meshing is yillustrated in the diagrammatic Views, Figs. 15 and 15a, and relates toa variation in the rate of the comeshing action outwardly across the toothzone N of the wheel, as between the upper part and the lower part of the tooth-faces. This is indicated in said gures in connec- .110

yt-ion with the radial lines showing the dif-y ferent circumferential arcs as measured on the circles, as measured, for instance on the circumference line 8, at the inner and outer Ends respectively'of the same pair of tooth- 115 aces.

ln the diagram, Fig. 15, the radial dotted lines 40 and 42, show the arc which is occupied (subtended)` on the inner circle 6, by

the inner end, or inclined prolefline, of the of the tooth 71.1. Similarly,

the radial dotted lines 41 and 43 show the relatively much smaller arc which is occupied on the outer circle 8 by the outer end,

or prole, of said tooth-.face fr'. The said 125 radial lines 42 and 43 include between tlem the arc (or angle), e* which represents the amount of the angular advance-circumfer- Y entially of the zone N,-of the lower line, Y

or baseline l of said face\f.5, from its inner end on circle 6 and passing outwardly to its outer end on circle 8. In like manner, the lines and 4l, on being compared, show the are (or angle), e3, which represents the amount 0f the angular advanceof the upper line, Z15, of said tooth-face f5 in passing from said circle 6 outwardly to said circle S; and from a comparison of the angles subtended by said arcs e3 and 6*, respectively, it will be seen that the said angular advance of the said upper face-line Z15 is very much' greater than that of the said lower face-line Z11. On the opposite tooth-face f3, the lo-wer line Z1G has the small angle 614 between the lines 52, 53, and the upper line Zl has the greater angle e111 between the lines 50, 5l, while the angles 5 and 15 show the similar but reversed circumferential arcs which include the two opposite-ly inclined faces f5 and f3, respectively. Thus the initial meshing occurs not only progressively, longitudinally and outwardly along the wheel-teeth, but takes place upon plane-surface skew-action tooth-faces, the surface elements of which have, respectively, an increasing circumferential advance from-the lower tooth-face line upwardly to the top line thereof, there- `by favoring the development in the opera- Z1", Z17 will Ybe parallel, and this principle also applies to each point along the height of the tooth-face.' These relations are further shown in the supplemental view, Fig.

15a, for making clear by comparison withA said Figs. 15 and 16 how the skew-angle of the toothface elements,-in this preferred construction,-progressively increases from the lower tooth-line or element, upwardly to the upper said element. The relatively small angular advance of the lower toothface line Z1?, from the inner circle 6 to the circle 8 (Fig. l5) is shown in Fig. 15a by the amount of the inclination of the line Z1S in the height of the tooth-face f5, thisamount corresponding to the arc e4, Fig. l5. Similarly, the larger angular advance of the upper tooth-face line Z15 is indicated by the amount of the inclination of the line Z10 in the height of the tooth-face, f5 (from point Z17 to point Z15, Fig. 155), this amount corresponding to the are e5. The said diagrammatic lines Z18 and Z1", are therefore drawn -on Fig. l5a for convenience in contrasting and comparing the described angular and circumferential advance of said lines Z15 and Z, with the similar angular advance which the vprole line ofl the said tooth-face has at the circle 8, at the outer end of the toothface f5.

When, the pitch-cone line m5 o f the pinion,see Figs. 8 and 20,-is inclined to and intersects the wheel-cone line this locates said pitch-cone line diagonally across the said plane-surface faces f3 and f5 of the wheel-tooth, it; then in the assembled wheels the depth of engagement of thev pinion teeth with said plane-surfaces of the wheelteeth outside of the pinion pitch-cone will be greatest at the inner ends, as at e1, and decreases toward the outer ends, as at e, of theteeth, for thereby modulating or conforming the coaction of the tooth-surface elements to those normal limits, as e1 and @15, of the zones of interference at the inner and outer tooth-circles, 6 and 8, respectively.

In Fig. 5the skew-circle t is shown located in the normal pitch-cone of the wheel B1 so that all the form axes, as x4, extend to said skew-circle t6.' In some cases, how ever, the skew circle may be located above, (elevated from) or may be located below, (depressed from) such normal location. rIlhese variations in the height of the location of the actual skew-circle, relatively to the center (as c, Fig. 6) of the wheel-including sphere D, are preferably restricted, in practice, to a moderate proportion of the radius of the normal-skew-circle; and the position of the actual skew-circle above or below the normal skew-circle may be .arranged, in any particular case, in such a manner-as to bring the said form-axis more nearly into alinement with the actual instant-axis of some co-meshing pinion of non-normal proportions relatively to the wheel-cone. These various features I have' particularly indicated in Fig. 6 where several skew-'circles are shown on a skewsphere, (Z, which has is center at c', coincident with the center o the wheel-including 105 sphere D. In the surface of said skew-circle sphere, the circle t6 is designated as the norrnal one, because it is located in the normal pitch-cone, this being the geometric cone whose apex is at the center c" of the wheel- 110 including 'sphere D, and whose outer circle, at 7 ,is the circle in which lie the axial-centers, as m4, etc. A slightly larger skewcircle t4 located on said small geometricKA sphere d is elevated above said normal skew- 115 circle, and one of the pairs of tooth-surfaces F5, is shown having its axis directed to this elevated skew-circle. A smaller skew-circle 15S is shown located on the skew-sphere d, in a depressed position, below said normal 120 skew-circle and (similarly as before) one of the pairs of tooth-surfaces F3, is shown `hav ing its axis directed tangentially to this depressed skew-circle. In this manner, especially whenthe (1o-meshing pinion is re'- 125 quired to be of an extreme non-normal proportion, the range of applicability of this system of bevel-gearing, may be somewhat extended as regards-its use in exceptional cases. When they form axis, as in Fig. 6, 130

two tooth-face planes, as f3 i generated) has verging longitudinally parallel extends to the sphere center o, then the skew-sphere is regarded as having been reduced substantially to zero, but not extinguished. 1n a pair of these gears, when the wheel 'has each longitudinally-parallel pair of tooth-faces with its center-line, as Fig. 3, in a plane radial to the wheel axis, the and f5 (see Fig. 15) have a skew angle relation ,to said wheel-axis, one of them, asics, having a torward skew while the other said face', as f3, has a rearward skew; similarly the pinion F has its tooth-faces arranged with their bounding planes (these coinciding with the \vheeltooth profile) ,-and hence their surtace elements in general,-located on similar skew-angles, and these in relatively the same order of arrangement, as indicated for instance, in Figs. l, 9 and 10. When the action-face, as f3, of the wheel has a rearward skew, (see Fig. 15) the amount of whichis indicated by the angle 613, the coacting pinion tooth-face will have a corresponding amount of skew in the said direction. 1n this pinion construction, therefore, the master-form (from or according to which the warped faces of the pinion teeth 'are to be the two side-planes in longitudinal parallelism, in this respect corresponding with the wheel construction. But when the wheel'has the inwardly-conplanes, (and therefore has the longitudinally parallel spaces, as F) the pinion master-form has,- relatively to the pinion-cone,-the outwardly-converging arrangement ofthe said longitudinally parallel planes, which are the form planes or bounding-planes of the curved-surface tooth-faces. In this improved form of the gearing, therefore, and as particularly indicated in Figs. 15, 15a and 19, there will be some one plane in which the sectional outline of the pinion tooth is a parallelogram, and this interseotingparallelogram or plane, may be said tobe the same as, or, geometrieally to coincide with, the similar plane of the wheel master-form, so that these two planes may Ibe said to come into the .same positions and geometrically coincide when the two engaging masterforms also come into coincidence in the same plane, and in the exact full-mesh position, this being also illustrated at Fig. 4;.

By reason of the sameness of organization as set forth of the master-forms of both wheel and pinion, and the reversal of the relative direction lof the convergence in the wheel and pinion, respectively, of a directlycoacting pair of these master-forms, (see Figs. 21, 23) when the counterpart tool (as T, Fig. 23) is employed for generating the pinion curved-surface tooth-faces, by the described compound-reproduction, it follows that this operation being begun at any one point, may then continue without change mi atea until the entire length of the tooth is completely shaped, and with `the result of torm-l ing the opposite tooth-faces of a 'transversely curved shape which has a constantly decreasing curvature along the length of the pinion tooth from the inner end toward the outer end thereof, and thereby producing on a conical pinion, a tooth characterized by the feature of having the opposite workingsurface primary elements (as indicated, for instance ati and e", Fig. 19) `in parallelism. In the pinion P4, Figs. 9, 10, the skewed teeth, gi are shown of that form.

An immediate and importantl practical result of this system` of parallel-construction as applied to both the pinion-teeth and wheel vtooth-space from identical masterform proiiles (in addition to the 4great advantage and ec'onomy,-as already eK- plained, of eliminating the compound-reproduction otherwise required for making the wheel teeth,) is the complete elimination of the diflicult setting and gaging operations which are necessary in the manufacture or conical gears having longitudinally-taper ing teeth on both wheel and pinion. Also in this parallel-construction, the pinion tooth may be completely shaped and sized without the danger of a variation in width of the tooth being caused by any inaccuracy in the indexing of the wheel blanks, when the teeth are made by cutting operations; thus 1 avoid one of the causes of imperfection appertaining to the manufacture of conical gearingl in -gear-toothgenerating machines, since hitherto, so far as1 l am aware, in such machines a single tool may operate only on one side of a tooth, whereas in this system, the master-form counterpart tool may' operate on both sides at the same time.

Fig. 16a illustrates the relation on the inner circle 6, of the pinion tooth, g, and a co-meshing wheel-tooth, 7L, when the tooth g is about to enter the meshing zone 7c! 1n Fig. 16b the same relation of the teeth g and h is shown as occurring on the outercircle 8. Whenv the inner en'd of the tooth comes to the line 6, as in Fig. 16, the outer end is normally, (in gears of low skew angles) about in the position g, Fig. 16". This rotative difference is approximately indi.- cated by the are e in Fig. 16, and by the dotted-line tooth-portion, g', in Fig. 16". 1n Fig. 17, a sectional side-view, as seen from the left-hand in Fig'. 16, illustrates how'the two teeth approachat an angle at the line 30, Fig. 16; and Fig. 18 illustrates `how the same teeth overlap when arriving at about the line 34 in Fig. 16.l On the opposite side of the meshing zone, of course, the teeth draw apart in a reverse order. The lines of the said progressive meshing and un-meshing, are indicated approximately at y34 and 35, respectively.

the line The features herein set forth as to the said parallelogram longitudinal section of the tooth-form and the straight line contact of the tooth-faces, are further illustrated in the geometrical diagram Fig. 19, which may be explained as follows: In these views,which show only a symmetrical case, in which the axes meet and coincide with the instant-axes,-the piniontooth is located in the-central and symmetrical position with reference to the plane of the shaft axes, and the pinion axis is so located as to have the axial skew-angle reduced to zero. In Fig. 19 the solid lines l, ZU and Z14 215 are the projections of the plane-surface tooth-faces of the masterwheel tooth-space, F (as in Fig. 4) looking in the direction of the common element or line of tangency of the twopitch cones, said common element being projected in the point Arcs of pitch circles of the master-wheel pitch-cone, at successive points in the toothzone N (drawn through different points in will be projected as the several arcs But all normals through points of contact must pass throu h point a: which is the instant-center projection of the instant-axis) for the relative motion of the pitch cones. The contact-normals,-refer ring now to the left-hand side of Fig. 19,- will therefore be projected inthe direction of line Z9, from the bearing line of which point 'i is a projection, to the form-axis line (which is also the instant-axis in the drawings as here shown) of which the point is the projection; and, (as indicated on the right hand side of Fig. 19,) all of the con-- tact-normals 'projected from the bearing-line of which the point z" is the projection will be projected in the direction of the line Z8, from the said line at point z" to the 'same axis-line at Hence the parallel straight projected lines, of which the points z' and i are projections, are lines of contact, and as such are common to the warped tooth-surface ofthe pinion and the plane tooth-sur-y faces of the master gear. The light lines g? and g5 and g3 indicate approximately the character of the pinion profile at successive points in its length. The figure of a section of the pinion-tooth taken on the lines z', i', when these are parallel and the plane (tangential) of the instant-axis, will have straightline sides, and when the instant-axis is parallel to the axial-line of the single-reproduction, (that is, when these lines coincide, as at a', Figs. 1 to 4, 6 and 22) this sectional figure will be a parallelogram. For positions other than the central (symmetrical) position shown in the Fig. 19, the common element of the rolling pitch-cones ,is a straightfline, since the master-wheel toothfaces are planes, and hence a set of normals from the former to the latter will intersect the latter at points lin a straight line. Hence the' contact lines are always straight lines. This maybe stated as follows: The pinion tooth-surface is the envelop of the lines of contact of the pinion tooth surface with a flat surface; that is, of the plane-surface `n1asterwheel tooth-face; the envelop of a inA this syscone has a face length less than the wheelcone face, I designate the pinion as being sub-normal, and when its said pinion cone-face exceeds the wheel-cone face, I designate the pinion as being plus-normal and I include the sub-normal and the plus-normal pinions under the term the pinion hasA the piniro-"P non-normal for broadly distinguishing them from those of normal proportions. A few such relative non-normal proportions are illustrated in Fig. 11, in which the smaller pinion P is sub-normal while the medium size pinion, P, is normal, and the larger pinions P and Ix are plus-normal. The medium pinion P is designated as normal because its proportions relatively vto the proportions of the mating wheel correspond to the proportions between wheel and pinion which would be necessary in bevelgear wheels of similar diameters when made according to the heretofore accepted stand-l ards; but in my improved bevel-gearing,- contrary to that former practice,-a.ll of the said pinions, although of widely varying sizes and lcone-lengths, operate correctly with the same mating whee1which thus becomes a master-wheel therefor.

In their tooth-face formation, each one of any plurality of the exchangeable pinions, as P, P', P2 and P3, Fig. 11, may have their tooth-face surfaces shaped by the method of compound-reproduction, or evolution, from and by the counterpart of the same master-wheel form F, by generating the pinion teeth fro-m a rolling movement on the pitch-cones. In this operation in the case of the smaller pinion P, the pitchcones resulting from the rolling movement will, of course, meet on the axial line at c; While in the case of the larger and P3, therolling movement uring ,the tooth-face generation will be on the gone pitch-surfaces having their apexes at c2and c3, respectively. In each case, however, the

same plane-surface counterpart tool, as" T.v

(see Figs. 21 to 23), or a suitable correspondingly-shaped cutte\(not shown) 1n 

